Finite-Time Tracking Control for a Class of Uncertain Strict-Feedback Nonlinear Systems With State Constraints: A Smooth Control Approach

Neuro-Adaptive-Based Fixed-Time Composite Learning Control for Manipulators With Given Transient Performance

This article investigates an adaptive neural network (NN) control technique with fixed-time tracking capabilities, employing composite learning, for manipulators under constrained position error. The first step involves integrating the composite learning method into the NN to address the dynamic uncertainties that inevitably arise in manipulators. A composite adaptive updating law of NN weights is formulated, requiring adherence solely to the relaxed interval excitation (IE) conditions. In addition, for the output error, instead of knowing the initial conditions, this article integrates the error transfer function and asymmetric barrier function to achieve the specific performance for position error in both steady and transient states. Furthermore, the fixed-time control methodology and Lyapunov stability criterion are synergistically employed in order to guarantee the convergence of all signals in the manipulators to a compact neighborhood around the origin within a fixed-time. Finally, numerical simulation and experiments with the Baxter robot results both determine the capability of the NN composite learning technique and fixed-time control strategy.

Composite Learning Adaptive Tracking Control for Full-State Constrained Multiagent Systems Without Using the Feasibility Condition

This article proposes a distributed consensus tracking controller for a class of nonlinear multiagent systems under a directed graph, in which all agents are subject to time-varying asymmetric full-state constraints, internal uncertainties, and external disturbances. The feasibility condition generally required in the existing constrained control is removed by using the proposed nonlinear mapping function (NMF)-based state reconstruction technology, and the Lipschitz condition usually needed in the consensus tracking is also canceled based on the adaptive command-filtered backstepping framework. The composite learning of the neural network-based function approximator (NN-FAP) and the finite-time smooth disturbance observer (DOB) provides a novel scheme for handling internal and external uncertainties simultaneously. One advantage of this scheme is that the use of online historical data of the closed-loop system strengthens the excitation of NN's learning. Another advantage is that the DOB with NN-FAP embedding realizes that the finite-time observation for external disturbance in the case of the system dynamics is unknown. A complete controller design, sufficient stability analysis, and numerical simulation are provided.

Observer-based event-triggered recursive optimal tracking control for a class of strict-feedback nonlinear systems

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness.

Predefined-Time Hierarchical Coordinated Neural Control for Hypersonic Reentry Vehicle

This paper investigates the predefined-time hierarchical coordinated adaptive control on the hypersonic reentry vehicle in presence of low actuator efficiency. In order to compensate for the deficiency of rudder deflection in advantage of channel coupling, the hierarchical design is proposed for coordination of the elevator deflection and aileron deflection. Under the control scheme, the equivalent control law and switching control law are constructed with the predefined-time technology. For the dynamics uncertainty approximation, the composite learning using the tracking error and the prediction error is constructed by designing the serial-parallel estimation model. The closed-loop system stability is analyzed via the Lyapunov approach and the tracking errors are guaranteed to be uniformly ultimately bounded in a predefined time. The tracking performance and the learning accuracy of the proposed algorithm are verified via simulation tests.

Adaptive Event-Triggered Finite-Time Control for Uncertain Time Delay Nonlinear System

In this article, adaptive event-triggered finite-time control is explored for uncertain nonlinear systems with time delay. First, to handle the time-varying state delays, the Lyapunov-Krasovskii function is used. Fuzzy-logic systems are used to deal with the unknown nonlinearities of the system. Notice that compared to the reporting achievements, our proposed virtual control laws are derivable by using the novel switch function, which avoids "singularity hindrance" problem. Moreover, the dynamic event-triggered controller is designed to reduce the communication pressure and we prove that the controller is Zeno free. Our proposed control strategy ensures that the tracking error is arbitrarily small in finite time and all variables of the closed-loop system remain bounded. Finally, to show the effectiveness of our control strategy, the simulation results are given.

Neural Adaptive Fixed-Time Control for Nonlinear Systems With Full-State Constraints

This article aims at this problem of adaptive neural tracking control for state-constrained systems. A general fixed-time stability criterion is first presented, by which an adaptive neural control algorithm is developed. Under the action of the proposed adaptive neural tracking controller, the tracking error converges into a small neighborhood around the origin in fixed time; meanwhile, all system states abide by the corresponding state constraints for all the time. The main difference between the present research and the previous control schemes for state-constrained systems is that this article proposes a novel and feasible approach to ensure that the constructed virtual control signals satisfy the state constraints on the corresponding states viewed as the virtual control inputs. Such an approach guarantees theoretically that all the system states cannot violate their constrained requirements at any time. Finally, two simulation examples provide support to the proposed results.

Adaptive Output Feedback Fuzzy Fault-Tolerant Control for Nonlinear Full-State-Constrained Switched Systems

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

Adaptive Neural Control of Nonlinear Nonstrict Feedback Systems With Full-State Constraints: A Novel Nonlinear Mapping Method

In this work, a neural-networks (NNs)-based adaptive asymptotic tracking control scheme is presented for a class of uncertain nonstrict feedback nonlinear systems with time-varying full-state constraints. First, we construct a novel exponentially decaying nonlinear mapping to map the constrained system states to new system states without constraints. Instead of the traditional barrier Lyapunov function methods, the feasible conditions which require the virtual control signals satisfying the constraint requirements are removed. By employing the Nussbaum design method to eliminate the effect of unknown control gains, the general assumption about the signs of the unknown control gains is relaxed. Then, the nonstrict feedback form of the system can be pulled back to the strict feedback form through the basic properties of radial basis function NNs. Simultaneously, the intermediate control signals and the desired controller are constructed by the backstepping process and the Nussbaum design method. The designed controller can ensure that all signals in the whole closed-loop system are bounded without the violation of the constraints and hold the asymptotic tracking performance. In the end, a practical example about a brush dc motor driving a one-link robot manipulator is given to illustrate the effectiveness of the proposed design scheme.

Adaptive Event-Triggered Neural Network Control for Switching Nonlinear Systems With Time Delays

The adaptive event-triggered-based neural network control is explored for switching nonlinear systems with nonstrict-feedback structure and time-varying delays in this article. First, the switching observer is designed to estimate the unmeasurable states. Due to the existence of time-varying input delay, a compensation system is introduced. The average dwell-time (ADT) scheme and the event-triggered controller are established. Furthermore, the semiglobal uniform ultimate boundedness (SGUUB) of all the variables in the closed-loop system is achieved and the Zeno behavior is avoided. Finally, the numerical simulation shows that our proposed control approach is effective.

Neural-Network-Based Adaptive Tracking Control for Nonlinear Multiagent Systems: The Observer Case

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

Adaptive Fuzzy Finite-Time Fault-Tolerant Consensus Tracking Control for High-Order Multiagent Systems With Directed Graphs

This article investigates the distributed adaptive fuzzy finite-time fault-tolerant consensus tracking control for a class of unknown nonlinear high-order multiagent systems (MASs) with actuator faults and high powers (ratio of positive odd rational numbers). The fault models include both loss of effectiveness and bias fault. Compared with existing similar results, the MASs considered here are more general and complex, which include the special case when the powers are equal to 1. Besides, the functions in this article are completely unknown and do not need to satisfy any growth conditions. In the backstepping framework, an adaptive fuzzy fault-tolerant consensus tracking controller is designed via adding one power integrator technique and directed graph theory so that the controlled systems are semiglobal practical finite-time stability (SGPFTS). Finally, numerical simulation results further verify the effectiveness of the developed control scheme.

Prescribed Finite-Time Adaptive Neural Tracking Control for Nonlinear State-Constrained Systems: Barrier Function Approach

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

Finite-Time Robust Intelligent Control of Strict-Feedback Nonlinear Systems With Flight Dynamics Application

The tracking control is investigated for a class of uncertain strict-feedback systems with robust design and learning systems. Using the switching mechanism, the states will be driven back by the robust design when they run out of the region of adaptive control. The adaptive design is working to achieve precise adaptation and higher tracking precision in the neural working domain, while the finite-time robust design is developed to make the system stable outside. To achieve good tracking performance, the novel prediction error-based adaptive law is constructed by considering the estimation performance. Furthermore, the output constraint is achieved by imbedding the barrier Lyapunov function-based design. The finite-time convergence and the uniformly ultimate boundedness of the system signal can be guaranteed. Simulation studies show that the proposed approach presents robustness and adaptation to system uncertainty.

Adaptive Fuzzy Finite-Time Control for Nonstrict-Feedback Nonlinear Systems

This article presents an adaptive fuzzy finite-time control (AFFTC) method for nonstrict-feedback nonlinear systems (NFNSs) with unknown dynamics. With the aid of the backstepping technique, by establishing the smooth switch function (SSF), a novel C¹ AFFTC strategy is recursively constructed, which counteracts the effect of nonstrict-feedback structure and unknown dynamics. Different from the reporting finite-time control achievements, the singularity hindrance derived from the differentiating virtual control law is availably surmounted. Moreover, the developed AFFTC strategy can drive the tracking error to converge into a small neighborhood of the origin in a finite time. Simulation results are conducted to substantiate the efficacy of theoretical findings.

Low-Cost Approximation-Based Adaptive Tracking Control of Output-Constrained Nonlinear Systems

For pure-feedback nonlinear systems under asymmetric output constraint, we present a low-cost neuroadaptive tracking control solution with salient features benefited from two design steps. In the first step, a novel output-dependent universal barrier function (ODUBF) is constructed such that not only the restrictive condition on constraining boundaries/functions is removed but also both constrained and unconstrained cases can be handled uniformly without the need for changing the control structure. In the second step, to reduce the computational burden caused by the neural network (NN)-based approximators, a single parameter estimator is developed so that the number of adaptive law is independent of the system order and the dimension of system parameters, making the control design inexpensive in computation. Furthermore, it is shown that all signals in the closed-loop system are semiglobally uniformly ultimately bounded, the tracking error converges to an adjustable neighborhood of the origin, and the violation of output constraint is prevented. The effectiveness of the proposed method can be validated via numerical simulation.